System and method for providing patient-specific dosing as a function of mathematical models updated to account for an observed patient response

ABSTRACT

A system and method for predicting, proposing and/or evaluating suitable medication dosing regimens for a specific individual as a function of individual-specific characteristics and observed responses of the specific individual. Mathematical models of observed patient responses are used in determining an initial dose. The system and method use the patient&#39;s observed response to the initial dose to refine the model for use to forecast expected responses to proposed dosing regimens more accurately for a specific patient. More specifically, the system and method uses Bayesian averaging, Bayesian updating and Bayesian forecasting techniques to develop patient-specific dosing regimens as a function of not only generic mathematical models and patient-specific characteristics accounted for in the models as covariate patient factors, but also observed patient-specific responses that are not accounted for within the models themselves, and that reflect variability that distinguishes the specific patient from the typical patient reflected by the model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/919,247 filed on Jul. 2, 2020, which is a continuation of Ser. No.16/271,528, filed on Feb. 8, 2019 (now U.S. Pat. No. 10,740,687), whichis a continuation of U.S. patent application Ser. No. 15/730,112 filedon Oct. 11, 2017 (now U.S. Pat. No. 10,268,966), which is a continuationof U.S. patent application Ser. No. 14/457,601 filed on Aug. 12, 2014(now U.S. Pat. No. 10,706,364), which is a continuation of U.S. patentapplication Ser. No. 14/047,545 filed on Oct. 7, 2013 (now U.S. Pat. No.10,083,400), which claims the benefit under 35 U.S.C. § 119(e) ofpriority to U.S. Provisional Application No. 61/710,330, filed on Oct.5, 2012, the entire disclosure and teachings of each of which isincorporated by reference herein.

FIELD OF THE INVENTION

The present invention relates generally to the administration ofmedications to live patients. More particularly, the present inventionrelates to a computerized system and method for processingmedication-specific mathematical models in view of observedpatient-specific responses to predict, propose and/or evaluate suitablemedication dosing regimens for a specific patient.

BACKGROUND OF THE INVENTION

A physician's decision to start a patient on a medication-basedtreatment regimen involves development of a dosing regimen for themedication to be prescribed. Different dosing regimens will beappropriate for different patients having differing patient factors. Byway of example, dosing quantities, dosing intervals, treatment durationand other variables may be varied. Although a proper dosing regimen maybe highly beneficial and therapeutic, an improper dosing regimen may beineffective or deleterious to the patient's health. Further, bothunder-dosing and over-dosing generally results in a loss of time, moneyand/or other resources, and increases the risk of undesirable outcomes.

In current clinical practice, the physician typically prescribes adosing regimen based on dosing information contained in the packageinsert (PI) of the prescribed medication. In the United States, thecontents of the PI are regulated by the Food and Drug Administration(FDA). As will be appreciated by those skilled in the art, the PI istypically a printed informational leaflet including a textualdescription of basic information that describes the drug's appearance,and the approved uses of the medicine. Further, the PI typicallydescribes how the drug works in the body and how it is metabolized. ThePI also typically includes statistical details based on trials regardingthe percentage of people who have side effects of various types,interactions with other drugs, contraindications, special warnings, howto handle an overdose, and extra precautions. PI s also include dosinginformation. Such dosing information typically includes informationabout dosages for different conditions or for different populations,like pediatric and adult populations. Typical PIs provide dosinginformation as a function of certain limited patient factor information.Such dosing information is useful as a reference point for physicians inprescribing a dosage for a particular patient.

FIG. 1 is a flow diagram 100 illustrating a method for developing amedication dosing regimen for a patient that is exemplary of the priorart. As shown in FIG. 1, a typical method involves identifying a patienthaving patient factors specified in the PI, and then for the selectedmedication that the physician is choosing to prescribe, reviewing the PIdosing information, as shown at steps 102 and 104 of Figure. By way ofexample, PI dosing information for Diovan® brand valsartin, anangiotensin receptor blocker used in adults to treat high bloodpressure, heart failure, etc., which is manufactured and/or distributedby Novartis Corporation of Summit, N.J., USA provides, in part, thefollowing dosing information: the type of patient for whom themedication is suitable (hypertensive patients), the types of patientsfor whom the drug should not be used (pregnant women, patients who arevolume or salt-depleted), a recommended initial dose (80 mg), arecommended does interval (once daily), and the approved range of dosesthat may be legally and/or ethically prescribed (80 to 320 mg).

Such dosing information is typically developed by the medication'smanufacturer, after conducting clinical trials involving administrationof the drug to a population of test subjects, carefully monitoring thepatients, and recording of clinical data associated with the clinicaltrial. The clinical trial data is subsequently compiled and analyzed todevelop the dosing information for inclusion in the PI. Systems,methods, process and techniques for gathering, compiling and analyzingdata to develop dosing information for inclusion in a PI are well-knownin the art and beyond the scope of the present invention, and thus arenot discussed in detail herein.

It should be noted that the typical dosing information is in a sense ageneric reduction or composite, from data gathered in clinical trials ofa population including individuals having various patient factors, thatis deemed to be suitable for an “average” patient having “average”factors and/or a “moderate” level of disease, without regard to many ofany specific patient's factors, including some patient factors that mayhave been collected and tracked during the clinical trial. By way ofexample, based on clinical trial data gathered for Abatacept, anassociated PI provides indicated dosing regimens with a very coarselevel of detail—such as 3 weight ranges (<60 kg, 60-100 kg, and >100 kg)and associated indicated dosing regimens (500 mg, 750 mg and 1000 mg,respectively). Such a coarse gradation linked to limited patient factors(e.g., weight), ignores many patient-specific factors that could impactthe optimal or near-optimal dosing regimen. Accordingly, it iswell-understood that a dosing regimen recommended by a PI is not likelyto be optimal or near-optimal for any particular patient, but ratherprovides a safe starting point for treatment, and it is left to thephysician to refine the dosing regimen for a particular patient, largelythrough a trial-and-error process.

Nevertheless, the physician then determines an indicated dosing regimenfor the patient as a function of the PI information, as shown at step106. For example, the indicated dosing regimen may be determined to be750 mg, every 4 weeks, for a patient having a weight falling into the60-100 kg weight range. The physician then administers the indicateddosing regimen as shown at 108. It will be appreciated that this may beperformed directly or indirectly, e.g., by prescribing the medication,causing the medication to be administered and/or administering a dose tothe patient consistent with the dosing regimen.

As referenced above, the indicated dosing regimen may be a properstarting point for treating a hypothetical “average” patient, theindicated dosing regimen is very likely not the optimal or near-optimaldosing regimen for the specific patient being treated. This may be due,for example, to the individual factors of the specific patient beingtreated (e.g., age, concomitant medications, other diseases, renalfunction, etc.) that are not captured by the parameters accounted for bythe PI (e.g., weight). Further, this may be due to the coarsestratification of the recommended dosing regimens (e.g., in 40 kgincrements), although the proper dosing is more likely a continuouslyvariable function of one or more patient factors.

Current clinical practice acknowledges this discrepancy. Accordingly, itis common clinical practice to follow-up with a patient after an initialdosing regimen period to re-evaluate the patient and dosing regimen.Accordingly, as shown in FIG. 1, the physician next evaluates thepatient's response to the indicated dosing regimen, as shown at 110. Byway of example, this may involve examining the patient, drawing blood oradministering other tests to the patient and/or asking for patientfeedback, such that the patient's response to thepreviously-administered dosing regimen may be observed by the treatingphysician. As a result of the evaluation and observed response, thephysician determines whether a dose adjustment is warranted, e.g.,because the patient response is deficient, as shown at step 112. Such adetermination may be made in accordance with existing medical treatmentpractices and is beyond the scope of the present invention, and thus notdiscussed here.

If it is determined at step 112 that a dose adjustment is not warranted,then the physician may discontinue dosing adjustments and the method mayend, as shown at steps 112 and 118.

If, however, it is determined at step 112 that a dose adjustment iswarranted, then the physician will adjust the dosing regimen ad hoc, asshown at 114. Sometimes the suitable adjustment is made solely in thephysician's judgment. Often, the adjustment is made in accordance with aprotocol set forth in the PI or by instructional practice. By way ofexample, the PI may provide quantitative indications for increasing ordecreasing a dose, or increasing or decreasing a dosing interval. Ineither case, the adjustment is made largely on an ad hoc basis, as partof a trial-and-error process, and based largely on data gathered afterobserving the effect on the patient of the last-administered dosingregimen.

After administering the adjusted dosing regimen, the patient's responseto the adjusted dosing regimen is evaluated, as shown at step 116. Thephysician then again determines whether to adjust the dosing regimen, asshown at 118, and the process repeats.

Such a trial-and-error based approach relying on generic indicateddosing regimens and patient-specific observed responses works reasonablywell for medications with a fast onset of response. However, thisapproach is not optimal, and often not satisfactory, for drugs that takelonger to manifest a desirable clinical response. Further, a protractedtime to optimize dosing regimen puts the patient at risk for undesirableoutcomes.

What is needed is system and method for predicting, proposing and/orevaluating suitable medication dosing regimens for a specific individualas a function of individual-specific characteristics that eliminates orreduces the trial-and-error aspect of conventional dosing regimendevelopment, and that shortens the length of time to develop asatisfactory or optimal dosing regimen, and thus eliminates or reducesassociated waste of medications, time or other resources and reduces therisk of undesirable outcomes.

SUMMARY

The present invention provides a system and method for providingpatient-specific medication dosing as a function of mathematical modelsupdated to account for an observed patient response. More specifically,the present invention provides a system and method for predicting,proposing and/or evaluating suitable medication dosing regimens for aspecific individual as a function of individual-specific characteristicsand observed responses of the specific individual to the medication.

Conceptually, the present invention provides access, in a direct way, tomathematical models of observed patient responses to a medication. Inprescribing an initial dose, the present invention allows for use ofpublished mathematical model(s) to predict a specific patient's responseas a function of patient-specific characteristics that are account forin the model(s) as patient factor covariates. Accordingly, theprescribing physician is able to leverage the model(s) in developing areasonably tailored initial dose for a specific patient, as a functionof the specific patient's characteristics, with much greater precisionthan a PI can provide.

To account for this uniqueness of any particular patient (BSV), thepresent invention allows for further use of the specific patient'sobserved response to the initial dosing regimen to adjust the dosingregimen. Specifically, the inventive system and method uses thepatient's observed response in conjunction with the publishedmathematical model(s) and patient-specific characteristics to accountfor BSV that cannot be accounted for by the mathematical models alone.Accordingly, the present invention allows observed responses of thespecific patient to be used refine the models and related forecasts, toeffectively personalize the models so that they may be used to forecastexpected responses to proposed dosing regimens more accurately for aspecific patient. By using the observed response data to personalize themodels, the models are modified to account for between-subjectvariability (BSV) that is not accounted for in conventional mathematicalmodels, which described only typical responses for a patient population,or a “typical for covariates” response for a typical patient havingcertain characteristics accounted for as covariates in the model.

Conceptually, the present invention allows the prescribing physician todevelop a personalized dosing regimen using one or more publishedmathematical models reflecting actual clinical data, without the loss ofresolution in the data and/or model that results from distillation ofthe actual clinical data into a relatively coarsely stratified set ofrecommendations for an “average” or “typical” patient, as in a PI.

The model-based development of such patient-specific medication dosingregimens eliminates or reduces the trial-and-error aspect ofconventional dosing regimen development. Further, such model-baseddevelopment shortens the length of time to develop a satisfactory oroptimal dosing regimen, and thus eliminates or reduces associated wasteof medications, time or other resources, as well as reduces the amountof time that a patient is at risk of undesirable outcomes.

Generally, the system and method involves gathering of mathematicalmodels developed from clinical data gathered from patients to whom aparticular medication had been administered, processing the models tocreate a composite model rich in patient data, and determiningpatient-specific dosing regimens as a function of patient-specificobserved response data processed in conjunction with data from themathematical model(s). More specifically, the system and method usesBayesian averaging, Bayesian updating and Bayesian forecastingtechniques to develop patient-specific dosing regimens as a function ofnot only generic mathematical models and patient-specificcharacteristics accounted for in the models as covariate patientfactors, but also observed patient-specific responses that are notaccounted for within the models themselves, and that reflect BSV thatdistinguishes the specific patient from the typical patient reflected bythe model.

BRIEF DESCRIPTION OF THE DRAWINGS

An understanding of the following description will be facilitated byreference to the attached drawings, in which:

FIG. 1 is a flow diagram illustrating an exemplary prior art method fordeveloping a medication dosing regimen for a patient;

FIG. 2 is a flow diagram illustrating an exemplary method for providingpatient-specific medication dosing as a function of mathematical modelsupdated to account for an observed patient response in accordance withan exemplary embodiment of the present invention; and

FIG. 3 is a schematic diagram of an exemplary system for providingpatient-specific medication dosing as a function of mathematical modelsupdated to account for an observed patient response in accordance withan exemplary embodiment of the present invention;

FIG. 4 is a series of graphs showing relationships between times sincelast dose (TSLD) and observed/predicted patient responses for sixteenexemplary patients;

FIGS. 5A-5D are exemplary graphs showing infliximab blood levelconcentrations as a function of time;

FIGS. 6A-6D are exemplary graphs illustrating an iterative Bayesianupdating process;

FIGS. 7A and 7B are exemplary graphs of blood level concentration as afunction of time, illustrating the impacts of Bayesian model averagingand updating;

FIGS. 8A-8D and FIGS. 9A-9E are exemplary graphs showing infliximabblood level concentrations as a function of rime;

FIGS. 10A-10F are exemplary graphs showing typical-for-covariates andpatient-specific forecasts of infliximab blood level concentrations as afunction of time, illustrating impacts of varying dose intervals; and

FIG. 11 is a system diagram showing an exemplary network computingenvironment n which the present invention may be employed.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a system and method for providingpatient-specific medication dosing as a function of mathematical modelsupdated to account for an observed patient response, such as a bloodconcentration level, or a measurement such as blood pressure orhematocrit. More specifically, the present invention provides a systemand method for predicting, proposing and/or evaluating suitablemedication dosing regimens for a specific individual as a function ofindividual-specific characteristics and observed responses of thespecific individual to the medication. Conceptually, the presentinvention provides the prescribing physician with access, in a directway, to mathematical models of observed patient responses to amedication when prescribing the medication to a specific patient. Inprescribing an initial dose, the present invention allows for use ofpublished mathematical model(s) to predict a specific patient's responseas a function of patient-specific characteristics that are account forin the model(s) as patient factor covariates. Accordingly, theprescribing physician is able to leverage the model(s) in developing areasonably tailored initial dose for a specific patient, as a functionof the specific patient's characteristics, with much greater precisionthan a PI can provide.

However, the forecasting and resulting dosing regimen based on themodel(s) is somewhat limited in that it is based on a hypotheticaltypical patient's response having the same patient characteristics.Accordingly, the forecasting and resulting dosing regimen is not likelyto be optimal because the published mathematical models cannot accountfor the patient's uniqueness, i.e. the fact that the patient's responseis likely to be unique and not typical. To account for this uniqueness,or between-subject variability (BSV), the present invention allows forfurther use of the specific patient's observed response to the initialdosing regimen to adjust the dosing regimen. Specifically, the inventivesystem and method uses the patient's observed response in conjunctionwith the published mathematical model(s) and patient-specificcharacteristics to account for BSV that cannot be accounted for by themathematical models alone. Accordingly, the present invention allowsobserved responses of the specific patient to be used refine the modelsand related forecasts, to effectively personalize the models so thatthey may be used to forecast expected responses to proposed dosingregimens more accurately for a specific patient. By using the observedresponse data to personalize the models, the models are modified toaccount for between-subject variability (BSV) that is not accounted forin conventional mathematical models, which described only typicalresponses for a patient population, or a “typical for covariates”response for a typical patient having certain characteristics accountedfor as covariates in the model.

Conceptually, the present invention allows the prescribing physician todevelop a personalized dosing regimen using one or more publishedmathematical models reflecting actual clinical data, without the loss ofresolution in the data and/or model that results from distillation ofthe actual clinical data into a relatively coarsely stratified set ofrecommendations for an “average” or “typical” patient, as in a PI.

The model-based development of such patient-specific medication dosingregimens eliminates or reduces the trial-and-error aspect ofconventional dosing regimen development. Further, such model-baseddevelopment shortens the length of time to develop a satisfactory oroptimal dosing regimen, and thus eliminates or reduces associated wasteof medications, time or other resources, as well as reduces the amountof time that a patient is at risk of undesirable outcomes.

Generally, the system and method involves gathering of mathematicalmodels developed from clinical data gathered from patients to whom aparticular medication had been administered, processing the models tocreate a composite model rich in patient data, and determiningpatient-specific dosing regimens as a function of patient-specificobserved response data processed in conjunction with data from themathematical model(s). More specifically, the system and method usesBayesian averaging, Bayesian updating and Bayesian forecastingtechniques to develop patient-specific dosing regimens as a function ofnot only generic mathematical models and patient-specificcharacteristics accounted for in the models as covariate patientfactors, but also observed patient-specific responses that are notaccounted for within the models themselves, and that reflect BSV thatdistinguishes the specific patient from the typical patient reflected bythe model.

In other words, the present invention provides a system and method thattakes into account variability between individual patients that isunexplained and/or unaccounted for by traditional mathematical models(e.g., patient response that would not have been predicted based solelyon the dose regimen and patient factors). Further, the present inventionallows patient factors accounted for by the models, such as weight, age,race, laboratory test results, etc., to be treated as continuousfunctions rather than as categorical (cut off) values. By doing so, thepresent system and method adapts known models to a specific patient,such that patient-specific forecasting and analysis can be performed, topredict, propose and/or evaluate dosing regimens that are personalizedfor a specific patient. Notably, the system and method can be used notonly to retroactively assess a dosing regimen previously administered tothe patient, but also to prospectively assess a proposed dosing regimenbefore administering the proposed dosing regimen to the patient, or toidentify dosing regimens (administered dose, dose interval, and route ofadministration) for the patient that will achieve the desired outcome.

Conceptually, observed patient-specific response data is effectivelyused as “feedback” to adapt a generic model describing typical patientresponse to a patient-specific model capable of accurately forecastingpatient-specific response, such that a patient-specific dosing regimencan be predicted, proposed and/or evaluated on a patient-specific basis.

Further, even before incorporating observed response data to adapt thegeneric model, the present invention allows for identification of aninitial dosing regimen that is better than would be suggested by a PI orany one mathematical model. More specifically, in one embodiment, aninitial dosing regimen is based on a composite model comprised of aplurality of patient data-rich mathematical models. In such anembodiment, the initial dosing regimen is more closely matched to aspecific patient's needs than a PI's generic recommendation for an“average” patient.

By refining a particular patient's initial dosing regimen as a functionof observed patient-specific data, in view of the composite mathematicalmodel, a personalized, patient-specific dosing regimen is developed, andfurther is developed quickly. It will be appreciated that the exemplarymethod is implemented and carried out by a computerized model-basedpatient specific medication dosing regimen recommendation system 200with input provided by a human operator, such as a physician, and thusacts as a recommendation engine and/or physician's expert systemproviding information for consideration by a prescribing physician.

An exemplary embodiment of the present invention is discussed below withreference to FIG. 2. FIG. 2 shows a flow diagram 150 illustrating anexemplary method for providing patient-specific dosing based not only onmathematical models describing responses for a population of patients,but also on observed response data for the specific patient to betreated. Referring now to the flow diagram 150 of FIG. 2, the exemplarymethod begins with providing a mathematical model-based patient-specificmedication dosing regimen recommendation system 200, as shown at 152. Anexemplary system 200 is shown in FIG. 3 and is discussed in detailbelow. By way of example, the system 200 may include conventionalhardware and software typical of a general purpose desktop,laptop/notebook or tablet computer. However, in accordance with thepresent invention, the system 200 is further specially-configured withhardware and/or software comprising microprocessor-executableinstructions for specially-configuring the system 200 to carry out themethod described below.

Referring again to FIG. 2, the method next involves providing at leastone mathematical model to the system, as shown at 154. In oneembodiment, the mathematical model is provided as part of a softwaremodule or library that is modular in nature, and that is manipulated bya software program comprising microprocessor-executable instructions forspecially-configuring the system 200 to carry out the method describedbelow. By way of example, these models may be pre-stored on the system,may be added to the system on a periodic basis, e.g., as part ofdistributed updates periodically stored on the system, or may bedownloaded from the Internet or another network on-demand, or otherelectronic media. Alternatively, the mathematical model may not be partof a software module or library, but rather may be hard-coded into, orotherwise be an integral part of, a unitary software program. In eithercase, the model is provided as input to the system, as shown at step154, FIG. 2, and is stored in the system's memory, e.g., in mathematicalmodel data store 218 a, FIG. 3.

Any suitable mathematical model may be used. A suitable mathematicalmodel is a mathematical function (or set of functions) that describesthe relationship between dosing regimen and observed patient exposureand/or observed patient response (collectively “response”) for aspecific medication. Accordingly, the mathematical model describesresponse profiles for a population of patients. Generally, developmentof a mathematical model involves developing a mathematical functionequation that defines a curve that best “fits” or describes the observedclinical data, as will be appreciated by those skilled in the art.

Typical models also describe the expected impact of specific patientcharacteristics on response, as well as quantify the amount ofunexplained variability that cannot be accounted for solely by patientcharacteristics. In such models, patient characteristics are reflectedas patient factor covariates within the mathematical model. Thus, themathematical model is typically a mathematical function that describesunderlying clinical data and the associated variability seen in thepatient population. These mathematical functions include terms thatdescribe the variation of an individual patient from the “average” ortypical patient, allowing the model to describe or predict a variety ofoutcomes for a given dose and making the model not only a mathematicalfunction, but also a statistical function, though the models andfunctions are referred to herein in a generic and non-limiting fashionas “mathematical” models and functions.

It will be appreciated that many suitable mathematical models alreadyexist and are used for purposes such as drug product development.Examples of suitable mathematical models describing response profilesfor a population of patients and accounting for patient factorcovariates include pharmacokinetic (PK) models, pharmacodynamic (PD)models, and exposure/response models, which are well known to those ofskill in the art. Such mathematical models are typically published orotherwise obtainable from medication manufacturers, the peer-reviewedliterature, and the FDA or other regulatory agencies. Alternatively,suitable mathematical models may be prepared by original research.

It should be noted that in a preferred embodiment, multiple mathematicalmodels for a single medication are provided as input to the system 200,to the extent they are available. Each mathematical model may be storedin the memory 218 of the system 200 as a mathematical function and/or inthe form of a compiled library module.

Next, the method involves identifying a specific patient havingpatient-specific characteristics, as shown at step 156. This step may beperformed by a physician or other human and may involve, for example,examination of a patient and gathering and/or measuring patient-specificfactors such as sex, age, weight, race, disease stage, disease status,prior therapy, other concomitant diseases and/or other demographicand/or laboratory test result information. More specifically, thisinvolves identifying patient characteristics that are reflected aspatient factor covariates within the mathematical model(s). For example,if the model is constructed such that it describes a typical patientresponse as a function of weight and gender covariates, this step wouldinclude identifying the patient's weight and gender characteristics(e.g., 175 pounds, male). Any other characteristics may be identifiedthat have been shown to be predictive of response, and thus reflected aspatient factor covariates, in the mathematical models. By way ofexample, such patient factor covariates may include weight, gender,race, lab results, disease stage and other objective and subjectiveinformation.

Next, the method involves providing the patient-specific characteristicsas input to the system 200, as shown at step 158. By way of example,this may be performed by a physician or other human operator of thesystem by providing input via a keyboard 208, mouse 210, or touchscreen, bar code/scanner, or other interface device 212 of the system200, as shown in FIG. 3. The patient-specific characteristics may bestored in the memory 218 of the system 200, in the form of a databaserecord, e.g., in patient factor data store 218 b of FIG. 3. Accordingly,the inputted patient characteristics can be used in conjunction with themodel(s) to identify a dosing regimen closely suited to a particularpatient's needs, as discussed below. More specifically, the inputtedpatient characteristics can be used in conjunction with the model(s) toidentify a dosing regimen that is “typical for covariates,” i.e., thatthe model(s) predict to be suitable for a typical patient having thespecific patient's covariate characteristics (e.g., for a typical 175pound male patient)—which is likely to provide a better dosing regimenthan a typical PI. The use of such models to develop the “typical forcovariates” dosing regimen is discussed below.

In this example, multiple different mathematical models describingpatient responses for a single medication are provided as input to thesystem 200. Accordingly, the system next performs Bayesian modelaveraging to develop a composite mathematical model as a function of themathematical models provided as input to the system, and thepatient-specific characteristics that are accounted for by the model(s)as patient factor covariates, as shown at step 160. More specifically,the multiple mathematical models for a single medication are thenprocessed by the system 200 to create a composite mathematical model forthe medication using Bayesian model averaging. The compositemathematical model may be stored in the memory 218 of the system 200,e.g., in RAM or in a composite model data stored 218 c, as shown in FIG.3.

Generally, Bayesian model averaging offers a systematic method foranalyzing specification uncertainty and checking the robustness of one'sresults to alternative model specifications. Bayesian model averagingaccounts for model uncertainty which can arise from poor parameterprecision, model mis-specification or other deficiencies that arise fromusing a single model. The standard practice of selecting a single modelfrom some class of models and then making inferences based on this modelignores model uncertainty, which can impair predictive performance andoverestimate the strength of evidence. Bayesian model averaging allowsfor the incorporation of model uncertainty into an inference. The basicidea of Bayesian model averaging is to make inferences based on aweighted average over a model space that includes several models. Thisapproach accounts for model uncertainty in both predictions andparameter estimates. The resulting estimates incorporate modeluncertainty and thus may better reflect the true uncertainty in theestimates. When several mathematical models have been published, theBayesian averaging of these models produces a weighted estimate ofpatient response, weighted relative to the amount of data used to createthe original individual models, the precision and performance of themodels, and the number of models combined in the Bayesian averagingstep, or alternatively weighting may be set by the user or incorporatedinto the system using a Markov-Chain Monte-Carlo (MCMC) approach. Thus,the development of a composite mathematical model from multiplemathematical models for a single medication compensates for limitationsthat may exist in any single model, and provides a more complete androbust mathematical model than is typically used in preparation of a PI.

Bayesian model averaging techniques are well known in the art. Themethods implemented for Bayesian model averaging vary depending on thetype of data and models being averaged, but most commonly are averagedusing a Markov chain Monte Carlo model composition (MC3) method. Adescription of exemplary methods used for Bayesian model averaging isprovided in Hoeting J A, Madigan D. Raftery A E, Volinsky C T. BayesianModel Averaging: A Tutorial. Statistical Science 1999, 14(4)382-417, theentire disclosure of which is hereby incorporated herein by reference.

Techniques for applying Bayesian averaging to mathematical models arewell-known in the art. By way of example, Bayesian averaging as amathematical technique is well-known in the contexts of politicalscience (see e.g., Bartels, Larry M. “Specification Uncertainty andModel Averaging.” American Journal of Political Science 41:641-674;1997), evaluation of traffic flow and accident rates (see e.g., DemirhanH Hamurkaroglu C “An Application of Bayesian Model Averaging Approach toTraffic Accidents Data Over Hierarchical Log-Linear Models” Journal ofData Science 7:497-511; 2009), and toxicology evaluations (see e.g.,Morales K H, Ibrahim J G, Chen C-H Ryan L M “Bayesian Model AveragingWith Applications to Benchmark Dose Estimation for Arsenic in DrinkingWater” JASA 101(473):9-17, 2006).

By way of further example, Bayesian model averaging is a method of usingmultiple mathematical models to make predictions, as is well known, forexample, in the field of weather forecasting, e.g., to predict atropical storm's most likely path as a function of different pathspredicted by different models. See, e.g., Raftery A E, Gneiting T,Balabdaoui F. and Polakowski M “Using Bayesian Model Averaging toCalibrate Forecast Ensembles” Mon. Wea. Rev., 133, 1155-1174; 2005.

Consistent with the present invention, a Bayesian model averagingapproach is used for forecasting patient response when multiple patientresponse models are available. An example involving Bayesian modelaveraging of multiple mathematical patient response models is shown inFIG. 7A. Referring now to FIG. 7A, the dashed red (A) and green (B)lines represent the expected concentration time profile from twodifferent mathematical models. The dashed red line (A) is derived afirst mathematical model as published by Xu Z, Mould D R, Hu C, Ford J,Keen M, Davis H M, Zhou H, “A Population-Based Pharmacokinetic PooledAnalysis of Infliximab in Pediatrics.” The dashed green line (B) isderived from a second mathematical model as published by Fasanmade A A,Adedokun O J, Ford J, Hernandez D, Johanns J, Hu C, Davis H M, Zhou H,“Population pharmacokinetic analysis of infliximab in patients withulcerative colitis.” Eur J Clin Pharmacol. 2009; 65(12):1211-28. In thisexample, concentration time profiles arising from both models areutilized and a composite model (shown in a dashed blue line (C))representing a weighted average is generated by Bayesian modelaveraging, as shown in FIG. 7A.

It should be noted, however, that the inventive method and system doesnot require multiple models as described in the example of FIG. 2. Inalternative embodiments, a single model may be used in lieu of acomposite model, and the corresponding Bayesian model averaging step(s)may be omitted.

It is further noted for clarity that one or more mathematical models canbe provided as input to and stored in the system 200 for each ofmultiple medications, though in the example of FIG. 2, only a singlemedication is discussed for illustrative purposes.

Referring again to FIG. 2, the system 200 next performs Bayesianforecasting to forecast typical patient responses for each of aplurality of proposed dosing regimens, as shown at step 162. This stepinvolves the system's use of Bayesian forecasting techniques to testdosing regimens for the specific patient as a function of thepatient-specific characteristics accounted for as patient factorcovariates within the models, and the composite mathematical model.Forecasted patient responses may be stored in he system's memory 218,e.g., in dose regimen forecast data store 218 e. This forecasting, basedon the composite model, involves evaluating dosing regimens based onforecasted responses for a typical patient with the patient-specificcharacteristics, which may be referred to as the “typical forcovariates” values. Techniques for applying Bayesian forecasting tomathematical models are well-known in the art.

Generally, Bayesian forecasting involves using mathematical modelparameters to forecast the likely response that a specific patient willexhibit with varying dose regimens. Notably, in this step theforecasting allows for determination of a likely patient response to aproposed dosing regimen before actual administration of a proposeddosing regimen. Accordingly, the forecasting can be used to test aplurality of different proposed dosing regimens (e.g., varying doseamount, dose interval and/or route of administration) to determine howeach dosing regimen would likely impact the patient, as predicted by thepatient-specific factors and/or data in the model/composite model.

In other words, this forecasting step involves use of the publishedmodels to evaluate dosing regimens to the extent that the publishedmodels are capable of evaluating dosing regimens, which is limited toanalysis for a typical patient having the specific patient's patientfactor covariates. While the resulting dosing regimen (corresponding toa satisfactory or best forecasted patient response) is likely moreaccurate than one that could be provided by a PI, it is not trulypersonalized for the specific patient being treated, as it does notaccount for unique characteristics of the patient being treated. Forexample, a specific 175 pound male patient may respond to a particulardosing regimen differently from a typical 175 pound male. Thus, thecomposite model is used to predict dosing regimens that would beexpected to be suitable and/or optimal for a typical patient with thepatient-specific characteristics.

More specifically, the system performs multiple forecasts of patientresponses to evaluate multiple proposed dosing regimens based on thepatient's characteristics, by referencing and/or processing thecomposite model. The system may determine each dosing regimen to beadequate or inadequate for meeting a treatment objective or targetprofile. For example, the target profile may involve maintenance of atrough blood concentration level above a therapeutic threshold. Further,the system may compare forecasts of patient responses to various dosingregimens, and create a set of satisfactory or best dosing regimens forachieving the treatment objective or target profile.

In one embodiment, the multiple proposed dosing regimens are provided asinput to the system by the user in a manual and/or arbitrary fashion.For example, the user may provide typed input to propose a dosingregimen to be evaluated, and in response the system will performBayesian forecasting to forecast the patient's response to the proposeddosing regimen. The user may subsequently provide other input to proposeanother dosing regimen to be evaluated. For example, the dose, doseinterval, and/or route of administration may be varied among theproposed dosing regimens to be evaluated. This is essentially atrial-and-error approach, albeit a sophisticated one based oncontinuous-function mathematical models accounting for patient factorcovariates, that permits the physician to test proposed dosing regimensagainst the composite model.

In another embodiment, the system follows an automated search algorithmto automatedly propose and test proposed dosing regimens to optimize thedosing regimen within the range of published clinical experience. In apreferred embodiment, the optimizing algorithm uses Bayesianforecasting, but proposes doses, dose intervals and/or routes ofadministration systematically. Regimens that achieve the desired goalare marked as feasible and stored by the system. The resulting output isa series of possible initial dosing regimens that are expected toachieve the desired clinical outcome, as predicted by the compositemathematical model and the patient factor covariates.

An illustrative example is provided below with reference to FIGS. 4A-4P.Referring now to FIGS. 4A-4P, patient response for each of 16 differentpatients (ID:1-ID:16) is shown as a function of time since the last dose(TSLD, hours). More specifically, the blue line (Y) is developed usingthe above-reference published mathematical model for infliximab (Xu etal). More specifically, each blue line (Y) is a plot of the average(“typical”) expected patient response predicted using the mathematicalmodel and the patient-specific factors (such as weight) that areprovided as covariates within the published model. Accordingly, thisblue line (Y) represents clinical data compiled for a plurality ofpatients, and is thus somewhat of an “average” or “typical”representation. Thus it can be seen in FIG. 4 that some individualpatient responses (open circle symbols) are higher than the blue line(as for ID:1 and ID:5) and other individual patient responses are lowerthan the blue line (as for ID:3, ID:7, and ID:9).

Therefore, the blue line (“typical for covariates”) recommendations arelikely better than a dosing indication in a PI, which often does nottake in account patient factors, or all of the important patientfactors, or may be based upon a coarse stratification of expectedpatient response. However, the blue line (Y) does not necessarilyprovide an optimal dosing regimen for a specific patient because it doesnot rake into account the variability in response seen between patientswith the same patient factors, sometimes referred to as thebetween-subject variability, or “BSV.” Thus, two patients with the samepatient factors may have different observed responses to a particulardose of a therapeutic drug as a result of variability that is notexplained by individual patient factors in the published model(s).

In accordance with the teachings herein, the inventive system wouldforecast patient responses for proposed dosing regimen(s) (FIG. 2B Step162) based on the blue line (Y) shown in FIG. 4A. Specifically for ID:3in FIG. 4, the initial dosing regimen provided by the system, based onlyon patient factors (covariates), would be expected to produce a responsereflective of the blue line.

Referring again to FIG. 4, the red lines (Z), discussed below, aredeveloped in accordance with the teachings of the present invention toaccount not only for patient-specific factors that are covariates withinthe model, but also for observed patient-specific responses consistentwith the present invention. More specifically, the red lines (Z) arebased upon mathematical models that have been Bayesian updated toreflect observed patient-specific responses. Thus, the red lines (Z) arelikely more representative of the proper dosing for the specific patientbeing treated. In accordance with the present invention, as discussed infurther detail below, subsequent dosing regimen recommendations (usingBayesian forecasting) for ID:3 would be based on the Bayesian updatedcomposite model (e.g. the solid blue line (D) in FIG. 7B or the red lineZ in FIG. 4) that accounts for the observed patient data (e.g. the opencircles), as discussed below.

Accordingly, in the example of FIG. 4, the blue (Y) and red (Z) linespredicted as patient responses for each patient ID:1-ID:16 aredifferent, based on the patient-specific factors that are covariateswithin the model and the observed patient-response data.

After performing one or more Bayesian forecasts to provide one or moreforecasted typical patient responses, the physician and/or the systemmay compare the various forecasted, so that an appropriate dosingregimen may be identified.

Referring again to FIG. 2, the exemplary method next involves the systemdetermining a recommended typical dosing regimen as a function of theforecasted responses, as shown at step 164. For example, the recommendedtypical dosing regimen may be selected by the system 200 as one of aplurality of Bayesian forecasts that were tested for achieving atreatment objective, based on feasibility and practicability, etc. Forexample, the recommended typical dosing regimen may be selected as theone of several tested/forecasted proposed dosing regimens that wereidentified as being able to maintain an exposure (i.e., drugconcentration) above a therapeutic level. For example, in FIGS. 10B-10F,for the “Difficult Patient”, multiple dose intervals were tested usingBayesian forecasting. As will be appreciated from FIGS. 10B-10F, theforecasting shows that dosing regimens including dose intervals of 1, 2and 4 weeks can maintain drug concentrations at a target level(represented by black dashed lines).

In one exemplary embodiment, the system 200 displays a list ofrecommended typical dosing regimens to a physician via its displaydevice 214, or causes the list of recommended dosing regimens to beprinted via an associated printer, or transmitted by electronic datatransmission via link 219 to a mobile computing device of the physician,a computing system of a pharmacy, hospital, clinic, patient, etc. Forexample, a selected subset of the testing dosing regimens (e.g., top 3,top 10, etc.) may be outputted by the system to the user as recommendedor suggested dosing regimens. It will be appreciated by those skilled inthe art that characteristics of the “best” dosing regimen will varyaccording to medication characteristics and/or treatment objectives.Accordingly, in the example of FIGS. 10B-10F, the dosing regimens forthe “Difficult patient” that were identified as being expected tomaintain concentrations (filled circles) above the target concentration(dashed lines) (i.e. the 1, 2, and 4 week dose interval) would bedisplayed, printed or transmitted as the recommended typical dosingregimen(s) of step 164.

In this exemplary embodiment, the physician may then browse therecommended typical dosing regimen(s) provided as output by the system,and then determine an initial dosing regimen for administration to thepatient. In doing so, the physician may select a dosing regimen from thelist, or may modify a recommended dosing regimen, in accordance with thephysician's judgment.

Various considerations may be taken into consideration by the physicianand/or the system in determining recommended dosing regimens and/orinitial dosing regimens. For example, a primary consideration may bemeeting a specific treatment objective, such as maintaining a minimumblood level concentration, maintaining a target blood pressure, etc.However, other considerations may also be taken into consideration, suchas ease of compliance, scheduling consideration, medication/treatmentcost, etc. The system may include utility functions for taking suchother considerations into account when determining the recommendedtypical dosing regimen(s).

The physician then directly or indirectly administers the initial dosingregimen, as shown at step 166. As compared with the techniques of theprior art discussed above with reference to FIG. 1, this initial dosingregimen is better-personalized to the specific patient to which it isadministered because it is based upon an interpretation of theunderlying composite mathematical and statistical model(s) as a functionof the patient's personal characteristics. In other words, the initialdosing regimen is reflective of a typical-for-covariates dosing regimendetermined by the model, and thus is suitable for a typical patienthaving the specific patient's characteristics. Accordingly, the initialdosing regimen is not based merely on a coarse interpretation of theunderlying model data as reflected in generic PI dosing information.Further, it is based upon forecasted outcomes following evaluations ofvarious doses, dose intervals and routes of administration, as part ofthe Bayesian forecasting process, and as a function of patientcharacteristics captured as patient factor covariates in a single model,or in a composite model produced by Bayesian model averaging of multiplemathematical models.

After an initial period, the physician in this exemplary methodfollows-up with the patient and evaluates the patient's response to theinitial dosing regimen and determines whether a dose adjustment iswarranted, e.g., because the patient response is deficient, as shown atsteps 168 and 170. These steps may be performed in a conventionalmanner, as discussed above with reference to FIG. 1. Accordingly, forexample, this may involve obtaining laboratory test results reflecting apatient's response to the administered dosing regimen, examining thepatient, and/or asking how the patient feels.

In this exemplary embodiment, if it is determined that a dose adjustmentis not warranted at 170, then dose adjustment is discontinued and themethod ends, as shown at 170, 186 and 188.

However, if it is determined that a dose adjustment is warranted at 170,then patient response data resulting from the evaluation is provided asinput to the system 200, as shown at 170 and 172. For example, suchinputting may include inputting quantitative and/or qualitative labresult test data and/or physician assessments into the system 200. Inaddition, patient characteristics which may have changed may also beevaluated and/or provided as input to the system. In particular, thisstep involves inputting updated observed measurements patient responseand updated patient-specific characteristics obtained from the specificpatient.

Optionally, the system ay be configured such that if a keyindividualized model parameter is more than ±3 standard deviations awayfrom the key typical parameter value, the system will indicate thatfurther use of this therapeutic drug in this patient may not bewarranted, because the specific patient's response suggests that thepatient will not respond sufficiently to the proposed treatment.

Referring again to FIG. 2, the system 200 next performs a Bayesianupdate to each of the underlying mathematical models, to update eachmodel as a function of the inputted patient-specific characteristics(tracked as patient factor covariates within the models) based on theinputted patient response data, as shown at step 174. Preferably, thisstep is performed using iterative Bayesian updating, and is furtherperformed immediately prior to the development and/or administration ofthe next dosing regimen. This updating with observed patient-specificdata takes into account the specific patient's observed response, andthus updates the model(s) to account for between subject variability(BSV) that is not accounted for in the models themselves. Accordingly,the application of Bayesian updating allows the software to account forchanging patient condition or patient factors, thus implicitlycorrecting the dosing regimen forecasts and recommendations.

Techniques for applying Bayesian updating to mathematical models arewell-known in the art. See, e.g., Duffull S B, Kirkpatrick C M J, andBegg E J Comparison of two Bayesian approaches to dose-individualizationfor once-daily aminoglycoside regimens Br J Clin Pharmacol. 1997; 43(2):125-135.

Generally, Bayesian updating involves a Bayesian inference, which is amethod in which Bayes' rule is used to update the probability estimatefor a hypothesis as additional evidence is obtained. Bayesian updatingis especially important in the dynamic analysis of data collected overtime (sequentially). The method as applied here uses models thatdescribe not only the time course of exposure and/or response, but alsoinclude terms describing the unexplained (random) variability ofexposure and response. It involves applying a “prior” to form theunderlying hypothesis. The “prior distribution” is the distribution ofthe parameter(s) before any data are observed. In our example, the priordistribution is the underlying series of mathematical models describingthe expected exposure and/or response following administration of amedication without the influence of observed individual patient data. Inour example, this would be the initial estimates generated for theinitial dosing regimen. The “sampling distribution” is the distributionof the observed data conditional on its parameters. This is also termedthe “likelihood,” especially when viewed as a function of theparameter(s) and is the observed response data. The marginal likelihood(sometimes also termed the evidence or the “posterior”) is thedistribution of the observed data marginalized over the parameter(s). Inour example, this would be the models after being updated by the inputobserved response data. Thus, Bayes' rule can be applied iteratively.That is, after inputting the observing response data, the resultingposterior probability can then be treated as a prior probability for thenext observed response, and a new posterior probability computed fromnew evidence. This procedure is termed “Bayesian updating.” The resultof Bayesian updating is a set of parameters conditional to the observeddata. The process involves sampling parameters from the priordistribution (in our example, this is all of the underlying models) andcalculating the expected responses based on the underlying models. Foreach underlying model, the difference between the model expectation andthe observed data is compared. This difference is referred to as the“objective function.” The parameters are then adjusted based on theobjective function and the new parameters are tested against theobserved data by comparing the difference between the new modelexpectation and the observed data. This process runs iteratively untilthe objective function is as low as possible (minimizing the objectivefunction) suggesting that the parameters are the best to describe thecurrent data. All underlying models are thus subjected to Bayesianupdating. Once all models have been updated, Bayesian averaging isconducted and a new composite model is produced.

In order to ensure that a global minimum of the objective function hasbeen obtained, the method may involve use of a random function tointerjects some variation in the process to ensure the objectivefunction surface is adequately explored and that a true global minimum(and not a local minimum which would not reflect the best description ofthe observed patient response data) has been achieved. The use of arandom function to ensure that a model achieves a true global minimum iswell-known in the field of stochastic approximation expectation methods.However, it is believed that the use of such a random function is novelin the context of Bayesian updating.

For illustrative purposes, an example involving iterative Bayesianupdating is discussed below with reference to FIGS. 6A-6D for a simpleexemplary model involving three parameters (CL, V and σ). Referring nowto FIGS. 6A-6D, the numbers below each Figure represent the likelihood(li) of the parameters where the likelihood is the probability of theobserved data (y_(ij)) given the selected model parameters (Θ_(i)σ_(i))at each iteration {li=P(y_(ij)|Θ_(i)σ_(i))}. In the iterative process,the system initially tests the prior (typical) parameter values (CL₁, V₁and σ₁. FIG. 6A) and calculates the function using these parametervalues. The system then compares the calculated value (curved line) tothe observed data (filled circles) and computes the likelihood (e.g.,shown below Figure A). The system then selects a different set ofparameters from a specified prior distribution to test (CL₂, V₂ and σ₂,FIG. 6B) and again calculates the function using the second set ofparameters. If the agreement between the observed data (filled circles)and predicted value (curved line) is better (e.g. the likelihood islarger) then the software will select a third set of parametersfollowing the same trend as was used for the selection of the second setof parameters. So if the second set of para ers was smaller than thefirst set of parameters, the third set of parameters will be stillsmaller (lower) in value. If the agreement between the observed data andpredicted function is worse (e.g. the likelihood is smaller), the systemwill automatedly select a different path, in this case picking newestimates that are larger than the second parameters but smaller thanthe first parameters. This process repeats iteratively until the systemcannot further improve the agreement between observed and predictedvalues (CL₄, V₄ and σ₄, FIG. 6D). It should be noted that not allparameters necessarily trend in the same way—some parameter values maybe larger than the initial values and some parameter values may besmaller.

Referring again to FIG. 2, the system 200 next performs Bayesian modelaveraging to develop an updated patient-specific composite model fromthe updated underlying models, as shown at step 176. This Bayesianaveraging process is similar to that described above with reference tostep 160, although the Bayesian averaging in this step 176 is performedon the underlying updated models that were updated based on observedpatient responses. The Bayesian averaging in step 176 produces anupdated composite model. By way of example, the updated model may bestored by the system in memory 218, such as in updated model data store218 d. At this point, the updated patient-specific composite modelparameters obtained are reflective of the observed response of thespecific patient being treated, and thus more accurately reflects theindividual patient, and incorporates variation as to response that isnot explained by patient factors, such as age and weight. Thus, theupdated patient-specific composite model better represents the expectedpatient response to subsequent doses.

This is reflected in the examples of FIGS. 4 and 7. Referring again toFIG. 4, after administration of the initial dose to ID:3 and obtainingobserved responses from patient ID:3, the individual patient response(open circles) would be shown to have deviated from the average expectedresponse (blue line, Y), The model(s) for ID:3 would then be updated(using Bayesian updating) based on the observed response for patientID:3 and combined into a composite model (using Bayesian averaging). InFIG. 7B, the result of Bayesian updating and Bayesian model averaging isshown. The dashed green line (E) is the Fasanmade model before Bayesianupdating, the solid green line (F) is the Fasanmade model after Bayesianupdating, the dashed red line (G) is the Xu model before Bayesianupdating, the solid red line (H) is the Xu model after Bayesianupdating, the dashed blue line (I) is the Bayesian averaged model beforeBayesian updating, the solid blue line (D) is the Bayesian averagedmodel alter Bayesian updating, and the open circles are the observeddata after the administration of the initial dosing regimen. As can beseen in these figures, the solid blue line (D, updated composite model)is reflective of the observed data (open circles). Thus, it is theupdated composite model reflected in the solid blue line (D) that isused for the next prediction of a dosing regimen in accordance with thepresent invention.

Referring again to FIG. 2, the system 200 next performs Bayesianforecasting to forecast a patient-specific response for each of aplurality of proposed dosing regimens, as shown at 178. This forecastingis performed as a function of the patient characteristics and thepatient-specific composite model, which reflects observedpatient-specific response data. This generally involves the same processas described above with reference to step 162, although the updatedcomposite model is used in step 178. By way of example, this may involveusing Bayesian forecasting to test a plurality of proposed doses topredict patient response for each of the proposed doses, prior toadministration of the proposed doses to the patient. More specifically,such Bayesian forecasting uses the updated composite model to predictpatient response for each proposed dosing regimen.

Next, the system 200 determines a recommended patient-specific dosingregimen as a function of the forecasted patient responses, as shown atstep 180 of FIG. 2. Similar to the method described above with referenceto step 164, the process of determining the recommended patient-specificdosing regimen may involve a manual Bayesian forecasting process inwhich the system receives a proposed dosing regimen provided as input bya user and projects the associated expected response, or alternativelymay involve an automated search algorithm that automatedly selects andtests proposed dosing regimens to optimize the dosing regimen within therange of published clinical experience, by evaluating dose, doseinterval and route of administration in view of commercially availableproducts. For example, a list of recommended proposed patient-specificdosing regimens may be selected by the system from a plurality ofBayesian forecasts that were tested for achieving a pre-specifiedclinical target (in the examples of FIGS. 8 and 9, a specific targettrough concentration). By way of further example, the treatmentobjective may be predefined for each medication and may be stored by thesystem. For example, the treatment objective may be to maintain a bloodlevel concentration above a predefined therapeutic threshold.

Next, the physician reviews the recommended patient-specific dosingregimen information obtained from the system 200 and determines anadjusted patient-specific dosing regimen as a function of the forecastedresponses. This may involve reviewing the system's comparison ofmultiple forecasted responses and selecting or modifying one of therecommend patient-specific dosing regimens as an adjusted dosingregimen.

The impact of Bayesian forecasting as a tool to prospectively evaluatedosing regimens is discussed below for illustrative purposes withreference to FIGS. 8A-8G. FIGS. 8A-8G show dosing regimen adjustments ina patient with moderate disease, in which all other relevant patientfactors are average (the “population patient,” or “typical” patient forwhom the package insert drug labeling was based on). In these Figures,the shaded region is the target concentration, and the filled circlesare the individual forecasted concentrations. Accordingly, the observeddata are fit using the models (in this example, the Fasanmade et al. andthe Xu et al. models), the models are Bayesian updated, are thenaveraged (using Bayesian averaging) and the resulting composite model isused to forecast expected patient response troughs (a criticalconsideration for therapeutic benefit in this example) for that patientfor each proposed dosing regimen. The crosses are the forecastedconcentrations predicted based only on patient factors (typicalpredicted concentrations) (i.e., predicted by the model without Bayesianupdating and only as a function of model covariates), the red trianglesJ are actual administered doses, and the aqua triangles K are theforecast doses. FIG. 8A reflects the predicted trough concentrationsachieved with a proposed labeled dose (5 mg/kg every 8 weeks), aspredicted using Bayesian forecasting in step 176. It can be seen thatfor this patient with moderate disease, the labeled concentration doesnot maintain the concentrations above the target.

Referring now to FIG. 8B, a proposed dosing regimen of 6 mg/kg givenevery 8 weeks is tested as part of step 176, which providesconcentrations that are at the target level and might reflect the secondattempt a physician would try for a patient if they failed to respond toinitial therapy.

Referring now to FIG. 80, a proposed dosing regimen of 7 mg/kg givenevery 8 weeks is tested as part of step 176. As noted from FIG. 8C, thisproposed dosing regimen is forecasted to provide concentrations that areappropriately higher than the target concentration and might reflect thedoses tried for a third attempt at dosing this patient. Referring now toFIG. 8D, a proposed dosing regimen of 5 mg/kg dose given every 7 weeksis tested and the forecast result is shown in FIG. 8D to provideadequate concentrations.

For the example of FIGS. 8A-8D, it may be noted that over a treatmentinterval of 56 weeks, the 7 mg/kg dose given every 8 weeks (FIG. 8C)would utilize a total dose of 49 mg/kg whereas the 5 mg/kg dose givenevery 7 weeks would utilize a total dose of 40 mg/kg (FIG. 8D) whileproviding satisfactory results (namely maintaining a minimumconcentration), a 20% reduction in total administered dose, reflectingan added savings to the patient in cost and a higher margin of safetydue to the overall reduction in drug exposure. Accordingly, step 178 mayinvolve selection of the dosing regimen associated with FIG. 8D.

Another illustrative example is described below with reference to FIGS.5A-5D. Referring now to FIGS. 5A-5D, the filled circles representobserved blood level concentrations as the result of lab tests, etc.,the red line (W) is the target concentration as determined in this caseby peer reviewed publications and current clinical practice, and thesolid line (X) is the individual predicted concentration using theupdated composite model, as determined by the mathematical models asupdated in step 174 and as averaged in step 176, and the dashed line (V)is the typical predicted concentration (which is calculated given onlycovariate information without any updating, similar in concept to theblue line shown in FIG. 4, and referenced in FIG. 2 at step 160). FIGS.5A and 5B represent data from a patient with moderate disease (a“Population” or “Typical” patient), and FIGS. 50 and 5D represent datafrom a patient with severe disease (a “Difficult patient”).

In FIG. 5A, the solid and dashed lines X, V are superimposed becauseBayesian updating has not yet been done. In FIG. 5B, Bayesian updatinghas been completed and the updated combined model is now based oncovariates and on observed patient responses, as discussed above.Therefore, there is a difference between the typical-for-covariatesconcentration arising from the combined model with only patient factorinformation, and the patient-specific predicted concentration arisingfrom the updated composite based on patient factor information andobserved patient-specific patient-response data (i.e. the model hasundergone Bayesian updating in addition to Bayesian averaging).

Referring now to FIG. 5C, the difference between the observed (filledcircle) and typical predicted values (solid line, X) is more pronouncedbecause of the severe disease. In FIG. 5D, the shaded region W is thetarget concentration, the filled circles are the patient-specificpredicted concentrations that are predicted by the Bayesian updatedmodel, the crosses are the concentrations predicted based only onpatient factors (typical predicted concentrations and are thus basedonly on covariates within the model, and not as the result of Bayesianupdating), and the triangles are the actual administered doses.

In FIGS. 5C and 5D, it can be seen that the patient-specific predictedconcentrations taken just prior to dosing (i.e. trough concentrations,which is the metric for dosing in this example) are falling below thetarget concentration W that must be achieved for clinical response, asbest shown in FIG. 5D. It should be noted that thetypical-for-covariates (“average”) predicted concentrations (crosses,based on a forecast made without Bayesian updating) suggest that theconcentrations arising from the dose being evaluated should beappropriate in that the crosses are above the target level (red band)and the typical concentration are higher than the red line W, as shownin FIG. 5D. However, following Bayesian updating (filled circles, FIG.5D) of the model to update the models to account for patient-specificresponse data and between subject variability, the model shows that thatthe dose being evaluated is not appropriate as the blue dots are belowthe target concentration (red band, W), and thus the targetresponse/treatment objective will not be met.

Additional examples of evaluating dose regimens are discussed below withreference to FIGS. 9A-E. Referring now to FIGS. 9A-90, the figuresrepresent a dose adjustment in a patient with severe disease (a“Difficult Patient” who deviates substantially from the typical“Population Patient” shown earlier). In the these Figures, the shadedregion is the target concentration, the filled circles are theindividual predicted concentrations (based on the Bayesian updatedcomposite model), the crosses are the concentrations predicted basedonly on patient factors (typical predicted concentrations as reflectedby the models, accounting for patient factors—i.e., the typical withcovariates), the red triangles L are actual administered doses, the aquatriangles M are the forecast doses (i.e., Bayesian forecasted resultsbased on the composite model, accounting for patient factors, andupdated to reflect observed patient response/exposure data). FIG. 9Areflects the trough concentrations achieved with the labeled dose (5mg/kg every 8 weeks). It can be seen that for this patient with severedisease, the labeled dose does not maintain the concentrations above thetarget, so a physician considering whether to prescribe this dosingregimen would likely reject it, and try to find a dosing regimenforecasted to provide a better result for the particular patient beingtreated. Accordingly, the conventional need for the patient to try thisineffective regimen is thus avoided.

In FIG. 9B, a forecasted response for a proposed dosing regimen of 10mg/kg given every 8 weeks is shown. As will be noted from FIG. 9B, thisproposed dosing regimen forecasts concentrations that are below thetarget level, but might reflect the second attempt a physician would tryin a prior art treatment approach for a patient if the patient failed torespond. In FIG. 90, a forecasted response for a proposed dosing regimenof 20 mg/kg given every 8 weeks is shown. This dosing regimen mightreflect the third attempt that a physician would try to achieve responsein a patient in a prior art treatment approach. As can be seen, none ofthese dosing regimens utilizing doses given every 8 weeks would provideconcentrations that were above the target level. As a result of theforecasting provided by the present invention, these ineffective dosingregimens are avoided, and associated deleterious effects to the patientare avoided. Additionally, the patient may be provided with an effectivedosing regimen immediately, without the loss of associated time to testthese dosing regimens in the patient that are typical of prior arttreatment approaches.

FIGS. 9D and 9E show forecasted responses associated with more frequentdosing regimens. FIG. 9D is a forecasted response for a proposed dosingregimen of 5 mg/kg given every 4 weeks (which is also a viablealternative dose regimen for 5 mg/kg given every 8 weeks). It will beappreciated from FIG. 9D that in this dosing regimen concentrations donot rise above the target trough. Accordingly, this dosing regimen isnot satisfactory, and thus not optimal. In FIG. 9E, a forecastedresponse for a proposed dosing regimen of 10 mg/kg given every 4 weeksis shown. It will be appreciated from FIG. 9E that this dosing regimenprovides concentrations that are above the target level. Accordingly,the dosing regimen of FIG. 9E is satisfactory, and would be identifiedby the system 200 as an acceptable dosing regimen during the automateddose regimen evaluation because the expected concentrations are at orabove the target concentration (shaded line).

In accordance with the example of FIGS. 9A-9E, an appropriate dosingregimen would not have been identified by the physician until at least3-4 dose regimens had been tested in the patient in accordance withprior art treatment techniques. However, the inventive system allows thephysician to test the proposed dosing regimens in advance ofadministration to a patient, identifying dose regimens that are likelyto be successful prior to testing them in the patient.

After the system has determined a recommended patient-specific dosingregimen (which may be a list of recommended patient-specific dosingregimens) at step 180, the physician may then browse the recommendedpatient-specific dosing regimen(s) provided as output by the system, anddetermine an adjusted dosing regimen for administration to the patient.This may involve reviewing the system's comparison of multipleforecasted responses and selecting a dosing regimen that was forecastedto best meet a treatment objective and is also practicable and feasible.In doing so, the physician may select a dosing regimen from the list, ormay modify the recommended patient-specific dosing regimen, inaccordance with the physician's judgment. As described above, variousconsiderations may be taken into consideration by the physician and/orthe system in determining recommended dosing regimens and/or adjusteddosing regimens.

The physician then directly or indirectly administers the adjusteddosing regimen, as shown at step 182. For example, this may be done byrevising a prescription to increase or decrease a medication quantity,to increase or decrease a dosing interval, to change a route ofadministration, etc., and may be done by the physician directly orindirectly, as discussed above.

As compared with the techniques of the prior art discussed above withreference to FIG. 1, an the initial dosing regimen discussed above withreference to step 168, this patient-specific adjusted dosing regimen isbetter-personalized to the specific patient to which it is administeredbecause it is based upon an interpretation of the underlying compositemathematical and statistical model(s) as a function of the patient'spersonal factors, and also the patient's own response to initialtreatment. Further, it is based upon forecasted outcomes followingevaluations of various doses, dose intervals and routes ofadministration, as part of the Bayesian forecasting process, and as theresult of the updated model account for the observed patient-specificresponses and between-subject variability not accounted for in thepublished models. Accordingly, the adjusted dosing regimen is highlypersonalized to the specific patient's needs.

After a period of treatment using the adjusted patient-specific dosingregimen, the physician in this exemplary method follows-up with thepatient and evaluates the patient's response to the adjusted dosingregimen and determines whether a dose adjustment is warranted, e.g.,because the patient response is deficient, as shown at steps 184 and170. As discussed above, such evaluation may be performed by gatheringobservations and/or data in a conventional manner. Accordingly, forexample, this may involve obtaining laboratory test results reflecting apatient's response to the administered dosing regimen, examining thepatient, and/or asking how the patient feels.

If it is determined in step 170 that no dose adjustment is warranted,e.g., because the patient is responding satisfactorily, then the doseadjustment is discontinued and the exemplary method ends, as shown atsteps 186 and 188.

If, however, it is determined in step 170 that further dose adjustmentis warranted, e.g., because the patient's response is deficient orsub-optimal, then new patient response data may be input to the systemand the method may repeat, as shown at steps 170-184.

Because patient condition (disease stage or status) and demographics canchange over time, the system can be used to repeatedly update theoptimal dose based on each individual patient's updated condition andfactors, exposure and/or response behavior so dose can be adjusted tooptimal levels throughout the course of therapy, or the therapy can bediscontinued if adequate exposure cannot be achieved. Further, thesystem thus allows a physician to evaluate potential dosing strategies(increasing/decreasing dose, shortening/lengthening dose interval orboth) before administering the next dose of drug to the patient. Thisapproach allows a dosing regimen to be optimized (or nearly optimized)within 1-2 dosing regimen cycles, and allows continuous monitoring andselection of appropriate dosing regimens as the patient's conditionchanges during treatment. This approach is innovative because: it allowsthe treating physician to provide an initial dosing regimen that isadjusted broadly for known influential factors; the subsequent dosingregimens are adjusted based on each patient's individual behavior;dosing regimens can be optimized rapidly, allowing appropriate drugcoverage to be achieved more quickly than the current practice; putativedoses can be tested on a computer before administration to the patient;dosing regimens can be adjusted during therapy based on patientcondition as needed; and over-dosing and under-dosing can be avoided.

FIG. 3 is a block diagram of an exemplary physician's expert system(PES) (shown logically as a single representative server for ease ofillustration) 200 in accordance with the present invention. The PES 200includes conventional computer hardware storing and/or executingspecially-configured computer software that configures the hardware as aparticular special-purpose machine having various specially-configuredfunctional sub-components that collectively carry out methods inaccordance with the present invention. Accordingly, the PES 200 of FIG.3 includes a general purpose processor and a bus 204 employed to connectand enable communication between the processor 202 and the components ofthe FES 200 in accordance with known techniques. The PES 200 typicallyincludes a user interface adapter 206, which connects the processor 202via the bus 204 to one or more interface devices, such as a keyboard208, mouse 210, and/or other interface devices 212, which can be anyuser interface device, such as a touch sensitive screen, digitized entrypad, etc. The bus 204 also connects a display device 214, such as an LCDscreen or monitor, to the processor 202 via a display adapter 216. Thebus 204 also connects the processor 202 to memory 218, which can includea hard drive, diskette drive, tape drive, etc.

The PES 200 may communicate with other computers or networks ofcomputers, for example via a communications channel, network card ormodem 219. The PES 200 may be associated with such other computers in alocal area network (LAN) or a wide area network (WAN), and operates as aserver in a client/server arrangement with another computer, etc. Suchconfigurations, as well as the appropriate communications hardware andsoftware, are known in the art.

The PES' software is specially configured in accordance with the presentinvention. Accordingly, as shown in FIG. 3, the PES 200 includescomputer-readable, processor-executable instructions stored in thememory for carrying out the methods described herein. Further, thememory stores certain data, e.g. in databases or other data stores shownlogically in FIG. 3 for illustrative purposes, without regard to anyparticular embodiment in one or more hardware or software components.For example, FIG. 3 shows schematically storage in the memory 218 of thePES 200 mathematical model data in Mathematical Model Data Store 218 aas a library module, observed response and administered dose informationstored in Patient Factor Data Store 218 b, composite data models storedin Composite Model Data Store 218 c, updated models stored in UpdatedModel Data Store 218 d, and dosing regimen forecast results stored inDose Regimen Forecast Data Store 218 e.

In an alternative embodiment, the methods and systems described hereinare delivered as web services via a network computing model. In such anembodiment, the system may be implemented via a physician/user-operableclient device and a centralized server carrying out much of thefunctionality described above. Such an embodiment is described belowwith reference to FIG. 11, which is a system diagram showing anexemplary network computing environment 10 in which the presentinvention may be employed. Referring now to FIG. 11, the networkcomputing environment includes a PES server system 200 a operativelyconnected to a plurality of client devices 20, 40, 60, 80 via acommunications network 50, such as the Internet or a proprietarywireless mobile telephone network. The FES server system 200 a mayinclude hardware and software conventional for web/application servers,but is further configured in accordance with the present invention toprovide the processing functionality described above with reference toPES system 200, and for interacting with the client devices. By way ofexample, client devices may be a personal computer 20, a mobiletelephone/smartphone 40, or a tablet PC, which may have substantiallyconventional hardware and software for communicating with PES serversystem 200 a via the communications network 50. For example, suchdevices may be configured for accessing a website or web interfacemaintained by PES server system 200 a, such that the physician/user mayoperate the client device to provide input and/or receive outputdescribed above, and to communicate with the PES server system 200 awhich performs the associated processing described herein. In theseembodiments, the client devices may not require any special-purposesoftware; rather, all special-purpose software is incorporated into thePES server system 200 a, and the client devices are used merely tocommunicate with inventive PES server system 200 a.

Alternatively, the client device may be a smartphone, tablet PC or othercomputing device 80 configured with a specially-configured nativesoftware application running on the client device 80, and communicatingwith PES server system 200 a. In such an embodiment, some or all of thestructure and/or processing described above with reference to PES system200 may be provided at client computing device 80, which may be operateby the user/physician, and which may communicate with PES server system200 a to provide the functionality described herein.

Having thus described a few particular embodiments of the invention,various alterations, modifications, and improvements will readily occurto those skilled in the art. Such alterations, modifications andimprovements as are made obvious by this disclosure are intended to bepart of this description though not expressly stated herein, and areintended to be within the spirit and scope of the invention.Accordingly, the foregoing description is by way of example only, andnot limiting. The invention is limited only as defined in the followingclaims and equivalents thereto.

What is claimed is:
 1. A method for treating a patient with apersonalized therapeutic dosing regimen, the method comprising:accessing a processor coupled to a memory; receiving by the processor afirst model stored in the memory, the first model being configured toindicate responses of patients in a population to a therapeuticadministered to such patients based on a time course of exposure of thetherapeutic in blood of the patients in the population; receiving by theprocessor first data indicative of an exposure of the therapeutic in thepatient's blood after receiving a dose of the therapeutic, the exposureof the therapeutic being determined from a blood sample taken from thepatient; receiving by the processor second data indicative of one ormore characteristics specific to the patient, wherein the one or morecharacteristics are shared by patients in the population of the firstmodel; the processor having third data indicative of a target exposurethreshold of the therapeutic in the patient's blood; preparing apatient-specific model by performing, using the processor, a Bayesianupdate to the first model based on the first data and the second data,the patient-specific model providing a predicted time course of exposureprofile of the therapeutic in the patient's blood that accounts for thepatient's response to the first dose of the therapeutic; providing oneor more proposed dosing regimens to achieve the target exposure of thetherapeutic in the patient's blood, the one or more proposed dosingregimens based on the patient-specific model and the second data,wherein the memory further comprises a database coupled to theprocessor, and further comprising storing information indicative of theone or more proposed dosing regimens in the database; selecting, fromamong the one or more proposed dosing regimens, a patient-specificdosing regimen for the therapeutic; and administering the therapeutic tothe patient according to the selected patient-specific dosing regimen.2. The method of claim 1, wherein the time course of exposure of thetherapeutic in the patient's blood is a concentration of the therapeuticin the patient's blood.
 3. The method of claim 1, wherein parameters ofthe patient-specific model are stored in the memory.
 4. The method ofclaim 3, wherein the one or more characteristics specific to the patientcomprise at least one of: a body size indicator, gender, race, labresults, disease stage, disease status, prior therapy, concomitantlyadministered therapeutics, concomitant diseases, and demographicinformation.
 5. The method of claim 4, further comprising outputting asubset of the one or more proposed dosing regimens as updated dosingregimens.
 6. The method of claim 4, wherein the therapeutic isadministered to the patient on a first day, and the method furthercomprising receiving by the processor fourth data indicative ofconcentration of the therapeutic in the patient's blood in samples takenfrom the patient after the administration of the therapeutic.
 7. Themethod of claim 6, wherein at least one sample providing the fourth datais taken from the patient's blood on the first day.
 8. The method ofclaim 6, further comprising receiving an input signal indicative of thetarget exposure threshold of the therapeutic in the blood of thepatient; and periodically updating the patient-specific model stored inthe memory based on exposure of the therapeutic in one or moreadditional patient blood samples, until the target exposure threshold ofthe therapeutic in the blood of the patient is achieved.
 9. The methodof claim 8, comprising determining a revised dose based on whether thefourth data is above a predicted exposure level of the therapeutic inthe blood of the patient.
 10. The method of claim 8, comprisingadjusting the dosing regimen after updating the patient-specific modelby one or more of increasing dose and shortening dose interval.
 11. Themethod of claim 8, comprising adjusting the dosing regimen afterupdating the patient-specific model by one or more of decreasing doseand lengthening dose interval.
 12. The method of claim 11, wherein thefirst model and the patient-specific model include a PK model.
 13. Themethod of claim 12, wherein the first model is a composite modelprepared from a plurality of mathematical models derived from dataobtained from the patients in the population.
 14. The method of claim13, further comprising preparing the composite model using Bayesianmodel averaging.
 15. The method of claim 14, further comprisingperforming the Bayesian update on each of the plurality of mathematicalmodels.
 16. The method of claim 15, wherein performing the Bayesiananalysis further comprises performing Bayesian forecasting to forecast atypical patient's response for each of the one or more proposed dosingregimens based on the patient-specific model and the second data. 17.The method of claim 8, comprising calculating an updatedpatient-specific dosing regimen of the therapeutic by selecting a dosingregimen corresponding to a minimum of an objective function.
 18. Themethod claim 8, wherein the one or more proposed dosing regimenscomprises a therapeutic-dosing interval of less than 4 weeks.
 19. Themethod claim 8, wherein the one or more proposed dosing regimenscomprises a therapeutic-dosing interval of 8 weeks.
 20. The method ofclaim 19, wherein the therapeutic administered to the patient isinfliximab, and wherein the first dose of infliximab is determined by aBayesian composite model.
 21. The method of claim 20, wherein the firstdose of infliximab is 5-7 mg/kg and has a therapeutic-dosing interval of8 weeks.